William Cary Downing appeals from an order of the United States District Court for the Southern District of New York (Gerard L. Goettel, Judge) denying his motions to compel arbitration, to stay this action pending that arbitration and to enjoin the defendant from commencing parallel actions. We affirm and remand for further proceedings consistent with this opinion.

BACKGROUND

In February, 1982, Downing was hired by Merrill Lynch, Pierce, Fenner & Smith, Inc. (“Merrill Lynch”) as an account executive trainee and registered representative in its office in Savannah, Georgia. At the time of his employment, Downing signed a non-compete agreement. By that agreement, Downing pledged that if he left the firm, he would not for one year solicit any of Merrill Lynch’s customers whom he had served or whose names had become known to him while in Merrill Lynch’s employ. He also pledged that he would not remove from Merrill Lynch’s premises any of its records, including records of the names and addresses of the firm’s clients. The non-compete agreement provided that it should be construed and governed by New York law.

The agreement did not contain any provision for the arbitration of disputes between the parties. Nevertheless, Downing contends that an agreement to arbitrate existed by virtue of the fact that on November 16, 1981, he signed and filed a Form U-4 with the New York Stock Exchange (the “Exchange” or “NYSE”). By that form, which was also signed by an officer of Merrill Lynch, Downing agreed to “arbitrate any dispute, claim or controversy that may arise between me and my firm ... that is required to be arbitrated under the rules, constitutions or by-laws of the organizations with which I register....”

The Rules and Constitution of the New York Stock Exchange require arbitration in[*194] two circumstances. Rule 347 of the New York Stock Exchange requires that:

Any controversy between a registered representative and any member or member organization arising out of the employment or termination of employment of such registered representative by and with such member or member organization shall be settled by arbitration, at the instance of any such party, in accordance with the arbitration procedure described elsewhere in these rules, [emphasis added].

In addition, Article VIII, Section 1 of the Constitution of the New York Stock Exchange requires that:

Any controversy between parties who are members ... [or] member firms ... and any controversy between a non-member and a member ... or member firm . .. arising out of the business of such member .. . shall at the instance of any such party, be submitted for arbitration, in accordance with the provisions of the Constitution and the Rules of the Board of Directors.

Downing resigned from Merrill Lynch on June 8,1983 and immediately went to work for E.F. Hutton (“Hutton”) in Savannah. He took with him copies of Merrill Lynch documents containing confidential information furnished by customers concerning securities transactions with Merrill Lynch. Downing intends to use those documents to solicit business on behalf of Hutton.

On the day he left Merrill Lynch, Downing filed a complaint in the Southern District of New York seeking a declaratory judgment that his “controversy” with Merrill Lynch was arbitrable. He also sought, inter alia, to compel Merrill Lynch to arbitrate the controversy before the Exchange, pursuant to the Federal Arbitration Act, 9 U.S.C. §§ 1 et seq. (1976), and to enjoin Merrill Lynch from commencing litigation in any other court.

On June 9, 1983, the day following the filing of this action, Louis Fantacone, Resident Vice-President of Merrill Lynch, wrote Downing to request that he return any customer information that he might have in his possession and to note that Downing had agreed not to solicit securities business from the customers with whom he had contact while in Merrill Lynch’s employ. Downing contended before the district court that Merrill Lynch customarily seeks judicial enforcement of non-compete agreements against former account executives while opposing their demands for arbitration before the Exchange. He also stated that his Merrill Lynch Office Manager had threatened to pursue “legal proceedings” against him if he solicited Merrill Lynch customers. Finally, Downing observed that he filed a demand for arbitration with the Exchange on June 8th. So far as we can tell from the record, the Exchange has not acted on Downing’s request.

On August 18th, Judge Goettel denied Downing’s motions to compel arbitration, to stay the action pending that arbitration and to enjoin Merrill Lynch from commencing parallel actions against him. Judge Goettel based his ruling on our recent decision in Coudert v. Paine Webber Jackson & Curtis, 705 F.2d 78 (2d Cir.1983). This expedited appeal ensued. We affirm on different grounds and remand for proceedings consistent with this opinion.

DISCUSSION

At the outset, we address the district court’s holding that our decision in Coudert, supra, is dispositive of this case. Coudert held that a defamation claim by a former account executive against her former employer was not arbitrable under NYSE Rule 347. Judge Goettel read that decision as relieving Merrill Lynch of its duty to arbitrate since Downing’s dispute, like Coudert’s, arose after the termination of his employment. We disagree with his view of Coudert’s implication.

The result in Coudert stemmed in part from the fact that the dispute erupted after the employment relationship had ceased but also from the fact that the subject matter of the dispute may have concerned the employer-employee relationship but did not arise directly out of it. In the present case, the dispute between Downing and Merrill[*195] Lynch is over his employment contract and in particular over a clause purporting to affect his conduct after termination of the employment relationship. If the parties had an agreement to arbitrate, a dispute over such a contract term would clearly be arbitrable notwithstanding the time at which the dispute arose. In Coudert, the subject matter was a claim sounding in tort and the temporal aspects simply reinforced the quite natural doubts about whether such a dispute was covered by the purported promise to arbitrate. In the present case, the temporal aspect is an inevitable consequence of the contract clause in issue.

Downing seeks to compel arbitration under Section 4 of the Federal Arbitration Act, 9 U.S.C. § 4, and to stay the present action under Section 3, 9 U.S.C. § 3, pending that arbitration. Relief under Section 4, however, is available only to persons “aggrieved by the ... refusal of another to arbitrate under a written agreement for arbitration.” Unless Merrill Lynch commences litigation or is ordered to arbitrate this dispute by the Exchange and fails to do so, it is not in default of any arbitration agreement it may have with Downing. Absent such default, arbitration cannot be compelled under Section 4. Since he has no present right to compel arbitration, Downing is not entitled to a stay under Section 3.

Downing is, however, entitled to a declaratory judgment as to whether he had an agreement with Merrill Lynch to arbitrate disputes over an employment contract. While arbitration itself must await further steps by Merrill Lynch to enforce the non-compete agreement, the Fantacone letter establishes a sufficiently concrete dispute to permit an adjudication of whether there is a promise to arbitrate. See Maryland Casualty Co. v. Pacific Coal & Oil Co., 312 U.S. 270, 272-73, 61 S.Ct. 510, 511-12, 85 L.Ed. 826 (1941); Salomon Brothers, Inc. v. Carey, 556 F.Supp. 499, 500 (S.D.N.Y.1983). Because Judge Goettel did not decide this question and it was not briefed on appeal, we do not reach it. We therefore remand so that declaratory judgment can be entered on the matter of whether the Form U-4 constitutes an agreement to arbitrate. See Coenen v. R.W. Pressprich & Co., 453 F.2d 1209, 1211 (2d Cir.), cert. denied, 406 U.S. 949, 92 S.Ct. 2045, 32 L.Ed.2d 337 (1972).

Finally, we consider Downing’s request for an injunction prohibiting Merrill Lynch from initiating parallel litigation against him. Assuming arguendo that Downing’s dispute is arbitrable, we agree with Judge Goettel that an injunction would be unnecessary since Section 3 of the Federal Arbitration Act would allow Downing to obtain a stay of any such litigation pending arbitration. On this record, Section 3 seems more than adequate to ensure rapid and unobstructed enforcement of any arbitration agreement.

CONCLUSION

In light of the foregoing discussion, we affirm the denial of the motion to compel arbitration, the denial of a stay pending arbitration and the denial of a motion to enjoin Merrill Lynch from instituting litigation against Downing. However, we remand for a determination of whether there is an agreement to arbitrate.